ET/BT rates of change - Page 3

by **another_jim** on Fri Sep 11, 2009 3:21 pm

popeye wrote:Now, i'm not saying that delta ET is a better predictor of delta BT than ET-BT. I am saying there is a strong correlation between delta ET and delta BT in the data I am recording.

Don't ever daytrade :wink:

Seriously, I think the patterns you are showing in the time domain graphs are correlated noise, something you try to filter out in data analysis. Your delta BT to ET - BT plot shows about an 80 percent correlation, just like mine, and is perfectly usable for coming up with a rough ET profile ahead of a roast.

Why not use fancier analysis to get a better prediction? You can be more precise if you get more complicated. When I take my roast data and run a simple regression of D30(BT) to two variables, BT and ET decoupled, I don't get a single (ET-BT) constant, but rather something more complicated (If the simple relation would hold, the intercept would be zero, and the ET coeffiecient would be 1 minus the BT coeffiecient).

Residuals:
     Min       1Q   Median       3Q      Max 
-7.24714 -1.15932  0.06123  1.34123  5.09404 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)    23.00764    0.94534   24.34   <2e-16 ***
BT              0.75874    0.01045   72.58   <2e-16 ***
ET              0.17964    0.01097   16.38   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 1.941 on 489 degrees of freedom
Multiple R-squared: 0.999,      Adjusted R-squared: 0.999 
F-statistic: 2.503e+05 on 2 and 489 DF,  p-value: < 2.2e-16

The correlation coefficient improves tremendously, going to 0.99, basically a perfect fit. The graph of predicted to actual points shows this:

However, this perfection is somewhat spurious. What happens if I find this equation for previous roasts, then apply it to the current one?

I'd get a perfectly shaped BT profile, but about 10 degrees darker than I wanted. This is normal, since small variations in dose or bean density change the heat transfer constants roast to roast. If you automate ET, you will always need some way to tweak the roaster real time, no matter how accurately you model the roasting process. Since I have to tweak in any case, I chose to use basic theoretical models rather than complex empirical ones, since the theoretical models are more intelligible, and more consistent when applied to new data.

by **popeye** on Fri Sep 11, 2009 5:18 pm

I was gathering my data by average the 1 second delta BT over the previous 45 seconds. This should be nearly the same as taking the delta over the previous 45 seconds. Just to make sure, I reran the data, with the y-values now the delta over the previous 45 seconds, multiplied by 4/3 to convert to degrees/min. here's the graph:

I've circled the data points that show the clearest correlation, just to make sure that I wasn't introducing an apparent correlation by adding a trendline that was improperly done. The black trendline simply averages the previous ten datapoints.

Again, peaks and valleys line up to the nearest couple of seconds. overall, delta BT decreases in relation to delta ET, but I can't explain away this data as noise. Noise would have a random, indiscriminate effect on the data, and actually destroy any correlation between the two graphs. The only way for the graphs to show correlation is for an unknown source to be affecting both delta BT and delta ET in a similar manner.

Notice what I said above: I'm not saying delta ET is driving delta BT. I'm saying that something is causing my ET thermocouple and my BT thermocouple to show similar responses in rate of change. I'm not even saying that my thermocouples are accurately recording ET and BT. (although my ET thermocouple is in the back of the hottop, approximately 1" from the top, and opposite the heating element, and my BT thermocouple is also in the back of hottop, protruding through the back wall 1.5" and as nearly centered in a 150g mass of beans (when hottop is rotating) as possible.)

So, since I doubt my actual beans are responding to heater cycles in the exact same fashion as the ET is, could my BT probe, despite being fully immersed in a mass of beans, be influenced by ET more than we commonly assume? Has anyone done any work on how accurate a BT probe is? It does seem like ET would still have a large effect on a BT probe - i mean the probe is taking glancing blows from the beans, but still surrounded by a lot of air.

Jim, I appreciate the feedback you're giving me (and please, let's continue to discuss this issue.) I hope that i'm not screwing up my calcs somehow - if anyone wants to see my spreadsheet, i'll email it out. If anyone has basic roast data, can you run your own data and plot delta ET and delta BT vs time to make sure i'm not screwing something up.

My working hypothesis for this data is that my BT probe (and possibly most BT probes) are unduly influenced by ET. If I can somehow prove this hypothesis, we can work on a correlation, as I discussed in a previous post. Can anyone throw some good reasons out there to discredit this hypothesis? I'm gonna try to set up some experimental runs to gather data.

by **another_jim** on Fri Sep 11, 2009 5:56 pm

What you are circling is correlated noise, i.e. the deviations from trend in one graph which ape those in the other. This isn't really information; it's artifacts. Large cyclic changes in temperatures at frequencies of a few seconds are not physically possible in a roaster, therefore these fluctuations show either noise or analysis artifacts.

I analyse data for a living. Here's the main lesson: alway focus on the underlying process. If the patterns you see cannot originate from that process, they are noise, artifacts of the measuring system or the data analysis. Pay attention to them, and you become a soothsayer, not a scientist. In a roaster, you are looking to create profiles that always have monotonic temperature increases in both ET and BT. You are looking to avoid non-monotonic, cyclic patterns which are the result of twitchy control. Unless you are using a ten gram roaster, these twitches will not have a frequencies lower than about 30 seconds to a minute. Moreover, they are exactly the things you are trying to avoid when roasting.

The Delta BT to (ET-BT) plot you posted is well behaved. You'll need to tweak the roaster in real time in any case no matter how you automate the ET, so why not use it to come up with your profile? It looks like to get a BT rate of rise of 10 degrees per ? You need to keep the ET about 40F above the BT, when you want a 20F rise, the ET needs to be 60F to 70F higher, and if the rise you want is 30 degrees per ?, you need an ET about 90 degrees higher.

What is wrong with using these as the rough benchmarks for your profiling, and doing the fine control on the fly as you roast? I guess I may be missing what you are trying to achieve.

by **popeye** on Fri Sep 11, 2009 8:58 pm

I'm happy enough with my last couple of roasts that I think i'll keep the on-the-fly control I have now, rather than turning it over to a PID.

Still, as to the artifacts that are showing up - those are not in the ET and BT, but rather in the delta ET and BT. While I agree the fluctuations would be too severe to be actual ET or BT responses, I think they are reasonable responses of the slope of ET to the heater fluctuations. As far as i understand, the HOTTOP uses digital proportional control - i.e. cycling of the heater on and off - to control the heat output. So while I expect to see the slope of ET oscillate up and down in response to heater on/off, I am surprised to see a highly correlated response in BT slope as well.

So, there may be errors in my calculations. The basic math is pretty simple and so is producing an excel graph. If i am screwing this up, can someone please do the same calcs with their own data?

Or, there may be artifacts - noise - impacting my data. But I've asked before: if it is noise, why is it impacting both graphs the same way. As far as I know, noise does not produce patterns -it produces randomness. (with the exception of some sort of electrical noise in my omega HH206RA that is injecting the same effect into both signals).

Or I have an unexplained anomaly in my data. I can dismiss it, and learn nothing. But i'm gonna continue to pull this thread until i get to the end of it. I thank all those of you who have been bouncing things back to me - primarily you, jim - and I'll post more here when I come up with something. I don't think i'm a soothsayer, I feel more like a scientist who has an unexplained observation and is seeking a model to explain it. But I hope in the end i'm not found to be just a guy who's bad with excel (and screwed something up.)

And yes, while I'm chasing the source of this artifact, my roasts are getting better too - that's the important part, right

Can someone with a HOTTOP please run a similar delta ET, delta BT vs. time graph?

by **popeye** on Fri Sep 11, 2009 9:04 pm

Ok Jim, I think i see your point about correlated noise - the noise deviation in both graphs is probably +/- 1 degree per second or so. So, the inherent noise makes anything that falls within that band useless as data. However, the black line averages the last ten datapoints, and the datapoints themselves represent averages of the slope over the previous 45 seconds. So the fact that the black lines are even more strongly correlated than individual datapoints indicates to me that as the effects of noise are reduced by averaging, the correlation shows even more strongly. Am i screwing something up in my logic there?

by **another_jim** on Fri Sep 11, 2009 10:01 pm

Spencer, I've said my piece.

by **another_jim** on Fri Sep 11, 2009 11:33 pm

OK, that may have sounded harsh. Let me try again.

You are trying to control a roast. If you log a roast every few seconds, and the graph of the temperature or its derivative is choppy, you either are looking at the data at too high a magnification or you have something changing temperature dramatically every few seconds. Can this be real?

It cannot. You may be picking up the cycling heater, or some micro climate in the roaster. Or the math routines in the spread sheet may be wonky. It doesn't matter. Have faith in the laws of physics and just ignore it.

You are trying to to create a profile that runs on a few segments, each several minutes long. So all this choppy stuff you are looking at is a pointless distraction. Look for correlations that hold over the entire roast.

by **cafeIKE** on Sun Sep 13, 2009 11:47 pm

another_jim wrote:The rate of change of bean temperature is proportional to the difference between bean and environmentla temperature. If you want an intereting plot take your data out of the time domain, and plot (ET(t)-BT(t)) on the X axis, and BT(t+x)-BT(t), i.e. delta BT, on the Y axis, if you get the time span of the delta right, yoiu'll see a nice straight line relationship.

I've update the Roast Plotter to include this graph
http://www.ielogical.com/coffee/RoastLogger.xls

by **another_jim** on Mon Sep 14, 2009 12:59 am

Thanks. The plot routines don't seem to work in the Open Office, something about missing basic libraries.

by **cafeIKE** on Mon Sep 14, 2009 10:22 am

Correct. I can port it to Open Office if there is interest.


Contact Us	Legal disclaimer and copyright: This content and all its parts are copyrighted, all rights reserved. Content including all text and images in part or in whole may not be reproduced in any electronic or printed medium without prior permission. Home-Barista, Home-Barista.com and related logos are trademarks of Home-Barista.com, LLC. Other trademarks are the property of their respective owners. By accessing this site, you agree to the terms of service. Overall speed: , current page: s, avg: s, max: s